Multimode optical fiber and methods of manufacturing thereof

ABSTRACT

The present invention generally relates to the field of fiber optics, and more particularly, to apparatuses, systems, and methods directed towards improving effective modal bandwidth within a fiber optic communication environment. In an embodiment, a multimode optical fiber in accordance with the present invention comprises a core and cladding material system where the refractive indices of the core and cladding are selected to modify the shape of the profile dispersion parameter, y, as a function of wavelength in such a way that the alpha parameter (α-parameter), which defines the refractive index profile, produces negative relative group delays over a broad range of wavelengths. The new shape of the profile dispersion parameter departs from traditional fibers where the profile dispersion parameter monotonically decreases around the selected wavelength that maximizes the effective modal bandwidth (EMB).

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/806,273 filed Jul. 22, 2015 which claims the benefit of U.S.Provisional Patent Application No. 62/029,659 filed Jul. 28, 2014, bothof which are incorporated herein by reference in its entirety.

FIELD OF INVENTION

The present invention generally relates to the field of fiber optics,and more particularly, to apparatuses, systems, and methods directedtowards improving effective modal bandwidth within a fiber opticcommunication environment.

BACKGROUND

The majority of optical channels utilized in premise networks such aslocal area networks (LAN) or storage area networks (SAN) utilizeintensity modulated lasers, where the transmitters modulate the power orintensity of the light. Vertical-cavity surface-emitting laser (VCSEL)transceivers widely deployed in data centers are examples of intensitymodulated transceivers, where on-off keying (OOK) is used. VCSELtransceivers have certain advantages including low cost, highreliability, and low power consumption compared to some other types oflasers used in communication systems.

Commercially available VCSEL transceivers with emission wavelengthsclosely centered around 850 nm, typically 850 nm±10 nm, can support datarates up to 10 Gbps and 14.025 Gbps for Ethernet and Fiber Channelapplications, respectively, for channel lengths less than 400 m.Moreover, industry standards for SAN operating at 25 Gbps and 28 Gbpsover reduced channel lengths are expected to be released in the future.However, there are limitations to increasing data rates using VCSELsoperating at a central wavelength of 850 nm.

As demand for higher data rates continues to grow, the pursuit of costeffective and efficient methods to increase transmission capacity areactively underway. The attributes of some of these transmission methodsinclude WDM, spatial division multiplexing using parallel fiber optics,and advance modulation formats that allow more spectral efficiency thanOOK. However, difficulties still exist when attempting to operate atincreased data rates. For example, for the aforementioned approaches itis challenging to make reliable VCSELs operating in the 850 nm spectralwindow fast enough to achieve data rates above 40 Gbps.

It is known by those skilled in the art that VCSEL modulation rates maybe increased via the incorporation of indium into material compositionof the laser quantum well structure. However, so doing results in theincrease of the laser emission wavelength.

Multimode fibers (MMFs) deployed in data centers and premises networksare currently optimized for a narrow spectral window around 850 nm, orless commonly around 1300 nm. These laser-optimized MMFs typically havea core diameter of about 50 μm and modal bandwidth (i.e., EMB) rangingfrom 2000 MHz·km to at least 4700 MHz·km when measured at 850 nm.

An important dispersive phenomenon in an MMF is a result of modal andchromatic dispersion, and can be described as follows. With respect tochromatic dispersion, a pulse launched into a given mode propagates at agroup velocity of the mode and if the pulse has a finite spectral width,the pulse spreads out in time due to material (or chromatic) dispersion.Chromatic dispersion is caused by the wavelength dependence of thematerial refractive index and results in a difference in propagationspeeds for each of the spectral components comprising the transmittedpulse. Chromatic dispersion increases with spectral width and inhigh-speed VCSELs, the RMS spectral width can be as broad as 0.65 nm.Consequently, in high-speed VCSEL-MMF channels, the chromatic dispersioncan become a significant penalty limiting the allowable reaches foraccurate transmission.

With respect to modal dispersion, when several mode groups are excitedand propagate through the fiber, the transmitted pulse broadens due todifferences in mode group velocities transporting the optical signal.These differences can be attributed to imperfections in the refractiveindex profile and/or differences between the ideal and actual operatingwavelength(s) of a transmitter. In laser-optimized fibers the refractiveindex profile is designed to equalize the mode group delays (or speeds)for the supported mode groups, thereby reducing modal dispersion andincreasing the modal bandwidth.

The parameter that describes the refractive index profile is theα-parameter, and the refractive index profile is often referred to asthe α-profile. In general, the refractive index profile is adistribution of refractive indices of materials within an optical fiberand for the core of an MMF the profile is defined by a function givenby:

$\begin{matrix}{{n(r)} = {n_{1}\sqrt{1 - {2{\Delta( \frac{r}{a} )}^{\alpha}}}}} & (1)\end{matrix}$where Δ≈(n₁−n₂)/n₁, n₁ is the refractive index on the axis of the fiber(i.e., at the center of the core), n₂ is the refractive index in thecladding, r is the radial position inside the fiber core, a is the coreradius, and a is the exponent parameter which typically takes a value of˜2 for fibers designed to support operation near 850 nm.

From equation (1), one can derive a simplified expression for therelative mode group delay t_(g) as a function of the wavelength and theα-profile parameters as shown:

$\begin{matrix}{{t_{g}(\lambda)} = {\frac{N_{1}(\lambda)}{c}\lbrack {{{\Delta( \frac{\alpha - {\alpha_{opt}(\lambda)}}{\alpha + 2} )} \cdot ( \frac{v_{g}}{v_{T}} )^{\alpha/{({\alpha + 2})}}} + \ldots}\mspace{14mu} \rbrack}} & (2)\end{matrix}$

where c is the speed of light in the vacuum, g is the mode group (MG)index (a mode group can comprise those modes that have nearly equalpropagation constants), v_(g) is the number of modes inside the MG thathave a propagation constant larger than β_(g)(v), v_(T) is the totalnumber of modes, N₁ is the group refractive index of the core materialat r=0 and, λ is the optical source wavelength.

The optimum alpha value α_(opt) that minimize group delay at a singleoperational wavelength λ and y the profile dispersion parameter aregiven by

$\begin{matrix}{{{\alpha_{opt}(\lambda)} = {2 + {y(\lambda)} - {\Delta\frac{( {4 + {y(\lambda)}} )( {3 + {y(\lambda)}} )}{5 + {2\;{y(\lambda)}}}}}}{{where},}} & (3) \\{{y(\lambda)} = {{- \frac{2\; n_{1}}{N_{1}}}\frac{\lambda}{\Delta}\frac{d\;\Delta}{d\;\lambda}}} & (4)\end{matrix}$

Using equations (2-4) the peak effective modal bandwidth valued of λ_(p)can be approximated to:

$\begin{matrix}{\lambda_{p} \approx {{- ( {\alpha - 2} )}( {\frac{2\; n_{1}}{\Delta\; N_{1}}\Delta\frac{d\;\Delta}{d\;\lambda}} )^{- 1}}} & (5)\end{matrix}$

The modal bandwidth of laser-optimized MMF is characterized by measuringits differential mode delay (DMD) or effective modal bandwidth; metricsstandardized within domestic and international standards organizationsand known to those skilled in the relevant art. The DMD test methoddescribes a procedure for launching a temporally short and spectrallynarrow pulse (reference pulse) from a single-mode fiber (SMF) into thecore of an MMF at various radial offsets. After propagating through theMMF, the pulses are received by a photodetector which captures the MMFcore power. After removal of the reference pulse temporal width, the DMDtemporal width can be determined at the 25% threshold level between thefirst leading edge and the last trailing edge of all traces encompassedbetween specified radial positions. The EMB is estimated by the Fourierdomain deconvolution of the input pulse from a weighted sum of thereceived signals for each radial offset launch. The set of weight valuesutilized in the computation can belong to a set of ten representativeVCSELs.

The relation between modal bandwidth, total bandwidth, and the fiberdesign parameters can be obtained from equation (2). In this equation,the magnitude of the term (α−α_(opt)) is proportional to the mode groupdelays and therefore inversely related with modal bandwidth. On theother hand the sign of (α−α_(opt)) determines the tilt or slope of thegroup delays with increasing radial offsets which is important for thecomputation of the modal-chromatic dispersion interaction (MCDI) andtotal bandwidth when this fiber is utilized with VCSEL basedtransceivers as described below.

To illustrate this concept and further clarify the meaning of the DMDslope and sign, consider the two simulated alpha-profile MMFs shown inFIG. 1. In this figure the horizontal axis is the relative time delays(ps/m) of the excited radial mode groups measured at the detector. Thevertical axis represents the mode group pulse waveform amplitude foreach radial offset of the SMF launch fiber. The lines inside each DMDpulse represent the discrete mode groups of the fibers, which areidentical in both DMD plots (a) and (b). For each DMD plot one cancompute a least square error (LSE) line connecting the pulses'centroids. The sign of the connecting line slope can be utilized toclassify the fibers as left-shifted (L-MMF) (i.e., negative slope), orright-shifted (R-MMF) (i.e., positive slope). Since the magnitudes ofthe slopes of the radial pulse centroids for these two simulated fibersare identical, the DMD and calculated modal bandwidth (EMB) are thesame.

For the L-MMF (negative DMD slope) higher order modes travel faster thanlower order modes as can be observed from their shorter arrival time tothe detector, herein referred to as negative relative group delay.Conversely, for the R-MMF (positive DMD slope) higher order modes travelslower than lower order modes.

In VCSEL-MMF channels the estimation of the total channel bandwidthdepends on the interaction of the spectral dependent coupling of theVCSEL modes to the fiber modes. This coupling produces a mode spectralbias (MSB), where shorter VCSEL wavelengths tend to couple into higherorder fiber modes and longer VCSEL wavelengths tend to couple into lowerorder fiber modes. Consequently, the difference in mode group delays isa result of both modal and chromatic dispersion effects. The effect ofMSB on group velocity is summarized Table I:

TABLE I MCDI: Effect of MSB in MMF mode speed. Spectra MMF Effect onModes MMF Mode Spectra Group Velocity Higher order Transport energy oflower regions of the Reduced modes VCSEL spectrum (Shorter wavelengths)velocity Lower order Transport energy of higher regions of the Increasedmodes VCSEL spectrum (Longer wavelengths) velocity

In general, MSB leads to MCDI which, depending on the α-profile, caneither increase or reduce the total channel bandwidth. In order toutilize MCDI to increase the channel bandwidth the group velocities ofthe higher-order modes (HOMs) must propagate faster than the lower-ordermodes (LOMs) when measured at the operational wavelength of the VCSELbased transceiver. This condition produces a DMD profile and slope signsimilar to the one shown in FIG. 1 for the L-MMFs. Since HOMs carry theshorter wavelengths of the VCSEL spectrum, it is possible to compensatefor their reduced speed caused by chromatic dispersion effects. Whencombined with the propagation speed of the LOMs, the resultant speeds ofthe modes tend to equalize as they propagate in the MMF. Thismodal-chromatic dispersion interaction and compensation has been furtherdetailed in Gholami A., Molin, D., Sillard, P., “Physical Modeling of 10GbE Optical Communication Systems,” IEEE OSA JLT, 29(1), 2011, pp.115-123; J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Investigationof the Interaction of Modal and Chromatic Dispersion in VCSEL-MMFChannels,” IEEE OSA JLT, 30(15), pp. 2532-2541; R. Pimpinella, J.Castro, B/Kose, and B. Lane, “Dispersion Compensated Multimode Fiber,”Proceeding of the 60th IWCS 2011; and J. Castro, R. Pimpinella, B. Kose,and B. Lane, “Mode Partition Noise and Modal-Chromatic DispersionInteraction Effects on Random Jitter,” IEEE OSA JLT, 31(15), pp.2629-2638, all of which are incorporated herein by reference in theirentirety. A summary of the effect of MSB on channel bandwidth ispresented in Table II:

TABLE II Effect of mode spectral bias and DMD slope sign on channelbandwidth. Fiber Without MSB With MSB L-MMF HOM propagate Reduced modegroup velocity differences faster than LOM between HOMs and LOMs.Improved bandwidth R-MMF LOM propagate Increased mode group velocitydifferences faster than HOM between HOMs and LOMs. Reduced bandwidth

By intentionally compensating for modal and chromatic dispersion,benefits in achievable channel reach and bit error rate (BER)performance in L-MMF compared to R-MMF have been modeled and observed.In MMF channels using VCSEL based transceiver, it has been shown thatMCDI can be used to not only reduce inter-symbol interference (ISI)penalties but also the mode partition noise (MPN). Conventional industrystandard link models predict that MPN becomes an important penalty forlonger reaches or higher data rates. An example of the improvements ofBER when using L-MMF is shown in FIG. 2. In particular, this figureshows measured BER performance of a 10 G VCSEL transceiver with 0.45 nmspectral width using two fibers with the same modal bandwidth of 4550MHz·km and the same length 550 m but with opposite sign on the groupdelay slope. The L-MMF is represented by the solid trace. The R-MMF isrepresented in the dash trace. Typical gains of 2.5 dB in the opticalbudget have been observed experimentally with modal-chromatic dispersioncompensated fibers depending on the running applications.

In MMF channels (such as for example VCSEL-MMF channels) operating athigher speeds, longer wavelengths, or in coarse-WDM (CWDM) systems, itwould be advantageous to preserve the modal-chromatic dispersioncompensation properties of current L-MMF. However, in conventional MMFs,the magnitude and sign of the mode group delay has high dependence onwavelength. Using current OM4 fibers it is not possible to maintain theL-MMF characteristics for the broad wavelength range required by CWDM.For example, assuming that an EMB of ≈4700 MHz·km is required by theapplication, the fiber behaves as L-MMF only in the spectral window of815 nm to 850 nm.

This is further described with reference to FIG. 3 which shows asimulated SiO₂ MMF doped with GeO₂ (4.5 mol %) in the core and fluorine(1% WT) in the cladding, where Δ≈0.01 at 850 nm. The utilized a valuefor this MMF is 2.049 which maximizes the EMB at λ_(p)=850 nm. Theprofile dispersion parameter and the optimum alpha are computed usingequations (3-4) and are shown, respectively, on the left and right ofFIG. 3. As can be seen from the figure, both of these values decreasemonotonically as a function of increasing wavelength. The maximum EMBoccurs at λ_(p)=850 nm, where α=α_(opt). This condition produces thecancellation of the modal dependent terms in equation (2). Therefore,the group delays are equalized for all mode groups. As the wavelengthvaries, α_(opt) becomes larger or smaller than α producing negative orpositive group delays as shown in equation (2). Therefore the same MMFcan behave as an L-MMF or an R-MMF depending on relative position of thewavelength with respect to λ_(p). More specifically, for wavelengthsbelow λ_(p) the DMD tilts to the left, as shown on the left side of FIG.1, and therefore the fiber can be classified as a L-MMF withmodal-chromatic dispersion compensation properties. On the other hand,for wavelengths over λ_(p) the DMD tilts to the right and the fiberbecomes a R-MMF, increasing total dispersion and degrading total channelbandwidth.

Using the mode group delays obtained via equation (2) and assuming thepower distribution of the modes for ten representative VCSELs asdescribed in the known DMD/EMB test standards, it is possible toestimate the EMB as a function of wavelength as shown in FIG. 4. Thismodel is illustrated for a typical MMF construction with λ_(p)=850 nmand indicates that L-MMF properties (shaded area) and thereforemodal-chromatic compensation can be provided in a limited spectral widththat is less than 40 nm.

The simulated behavior is consistent with multiple experiments performedusing MMFs of different grades: OM3 and OM4. In these experiments theEMB was measured at different wavelengths ranging from 800 nm to 960 nm,and the results of these measurements are shown in FIG. 5. In all cases,the L-MMF condition occurs only when the measured wavelength was belowthe λ_(p) of each fiber (wavelength for peak EMB of each fiber). When anEMB>4700 MHz·km is required the spectral window for L-MMF becomesrelatively limited.

An example of this characteristic is shown in FIGS. 6A and 6B whichillustrate a typical MMF using Ge as a main dopant to increase therefractive index in the core. This dopant produces a monotonicallydecreasing alpha optimum distribution as shown by the solid line in FIG.6A. When using α_(d) (illustrated by the dashed line) as the α-profilevalue for the fiber's refractive index, negative relative group delaysare attained when α_(d)<α_(opt). As a result, the high modal bandwidthfor negative relative group delays (or L-MMF condition) is maintainedfor a relatively narrow spectral region. This is shown in FIG. 6B wherethe negative relative group delays are exhibited to the left of the peakEMB wavelength.

Based on the foregoing, existing approaches do not provide means tooptimize modal bandwidth while at the same time produce MCDI for a broadrange of optical wavelength. As such, there is a need to provide animproved MMF capable not only for large modal bandwidth, but alsonegative t_(g) in a broad spectral window.

SUMMARY

Accordingly, at least in part the present specification is directedtowards MMF that can provide increased EMB and negative relative groupdelays in broad spectral regions of the fiber.

In an embodiment, the present invention provides a means to achievenegative relative group delay in a relatively broad spectral window.

In another embodiment, the present invention provides a method foroptimization of the modal bandwidth over a relatively broad spectralwindow which is an important factor in the channel dispersionlimitations.

In yet another embodiment of the present invention, an MMF is used toenable CWDM (unidirectional or bi-directional) in multimode channels inwhich multiple VCSEL transceivers transmit and receive datasimultaneously at different wavelengths.

In yet another embodiment of the present invention, an MMF is used forVCSEL transceivers operating at wavelength≥850 nm, where the speedproperties of the laser and chromatic dispersion of the fiber improvedata rate and reach.

In yet another embodiment, a multimode optical fiber in accordance withthe present invention comprises a core and cladding material systemwhere the refractive indices of the core and cladding are selected tomodify the shape of the profile dispersion parameter, y, as a functionof wavelength in such a way that the alpha parameter (α-parameter),which defines the refractive index profile, produces negative relativegroup delays over a broad range of wavelengths. The new shape of theprofile dispersion parameter departs from traditional fibers where theprofile dispersion parameter monotonically decreases around the selectedwavelength that maximizes the effective modal bandwidth (EMB).

In another embodiment, according to the principles of present invention,the dopants added to the fiber composition produce a concave or convexdispersion parameter profile with minimum value at or near to thewavelength λ_(p) which has the peak EMB. The convex or concave shape ofthe profile dispersion parameter, y, broadens the range in which thefiber provides the desired modal bandwidth. More importantly, dependingon the shape produced by y, the α-parameter is tuned to produce negativerelative high-order group delay in a broad band of wavelengths. Negativerelative high-order group delays result in the compensation of modal andchromatic dispersion in VCSEL channels which may enhance the totalbandwidth up to or above 50%.

In yet another embodiment, multimode fibers manufactured in accordancewith the present invention exceed the bandwidth provided by OM3 and/orOM4 fibers and at the same time compensate for modal and chromaticdispersion over a broad range of wavelengths. This can be useful intransceiver requirements for long wavelength VCSEL and/or coarsewavelength division multiplexed (WDM) systems.

In yet another embodiment, a MMF in accordance with the presentinvention provides higher channel bandwidth which translates to lowerISI and lower MTN penalties in VCSEL transceivers. Therefore, an MMFaccording to an embodiment of the present invention may enable fasterdata rates and/or longer reaches maintaining the cost and reliabilityadvantages of VCSEL-MMF channels.

In yet another embodiment, the present invention is an MMF for operatingwithin a spectral window, the MMF having one of a peak effective modalbandwidth or a minimum effective modal bandwidth at wavelength)λ_(p).The MMF includes a cladding having a refractive index of n₂, and a core,the core having a radius a and a refractive index profile comprised ofrefractive indices n(r) defined by a function of a radial distance rfrom a center of the core to a:

${n(r)} = {n_{1}\sqrt{1 - {2{\Delta( \frac{r}{a} )}^{\alpha}}}}$where n₁ is a refractive index at the center of the core, a is aparameter defining a shape of the refractive index profile, andΔ=(n₁−n₂)/n₁. The core further has an α_(opt) profile comprised ofvalues α_(opt)(λ) defined by a function of wavelength λ, where for agiven λ the α_(opt)(λ) value minimizes a group delay of the MMF when theα is set equal to α_(opt)(λ), the α_(opt) profile having one of aconcave shape with a maximum at α_(opt)(λ_(p)) or a convex shape with aminimum at α_(opt)(λ_(p)), where α≤α_(opt)(λ_(p)).

In yet another embodiment, the present invention is an MMF for operatingwithin a spectral window. The MMF includes a cladding having arefractive index of n₂, and a core, the core having a radius a and arefractive index profile comprised of refractive indices n(r) defined bya function of a radial distance r from a center of the core to a:

${n(r)} = {n_{1}\sqrt{1 - {2{\Delta( \frac{r}{a} )}^{\alpha}}}}$where n₁ is a refractive index at the center of the core, a is aparameter defining a shape of the refractive index profile. andΔ=(n₁−n₂)/n₁. The core further has an α_(opt) profile comprised ofvalues α_(opt)(λ) defined by a function of wavelength λ, where for agiven λ the α_(opt)(λ) value minimizes a group delay of the MMF when theα is set equal to α_(opt)(λ), the α_(opt) profile having one of aconcave shape with a maximum α_(opt) value or a convex shape with aminimum α_(opt) value, where α is less than or equal to the one of themaximum α_(opt) value or the minimum α_(opt) value.

In yet another embodiment, the present invention is an MMF for operatingwithin a spectral window. The MMF includes a cladding, and a core, thecore having a radius a and a refractive index profile, the corecomprising at least one dopant, a concentration of the at least onedopant varying between a center or the core and a. The spectral windowsis defined by an overlapping range of wavelengths (1) at which the MMFhas an EMB equal to or above a predefined minimum with one of a peak EMBor a minimum EMB occurring at wavelength λ_(p) which is less than amaximum wavelength of the spectral window and (2) at which adifferential mode delay (DMD) plot of the MMF exhibits a shift to theleft of its higher order modes relative to its lower order modes. TheDMD plot is measured by launching a plurality of optical pulses into oneend of the core at various radial distances r and observing an arrivalof the optical pulses at another end of the core at the various radialdistances r to determine a velocity of any one of the plurality ofoptical pulses launched into the core at some radial distance r relativeto any other of the plurality of optical pulses launched into the coreat some other radial distance r. And the shift to the left ischaracterized by some of the plurality of optical pulses having a fastervelocity relative to at least one other optical pulse having a slowervelocity, the at least one other optical pulse having a slower velocitybeing launched into the core at a lower radial distance r than any ofthe some of the plurality of optical pulses having a faster velocity.

These and other features, aspects, and advantages of the presentinvention will become better understood with reference to the followingdrawings, description, and any claims that may follow.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates DMD radial waveform plots for two fibers with equalradial mode group delays but opposite slope signs.

FIG. 2 illustrates an example of the improvements of BER when usingL-MMF.

FIG. 3 illustrates graphs of a profile dispersion parameter and α_(opt)for an exemplary MMF with λ_(p)=850 nm.

FIG. 4 illustrates an EMB modeled as a function of the wavelength fortypical MMF construction with λ_(p)=850 nm.

FIG. 5 illustrates the measured EMB as a function of the wavelength fortypical MMFs with several values of λ_(p) ranging from 800 nm to 960 nm.

FIG. 6A illustrates an alpha-profile MMF doped with Ge.

FIG. 6B illustrates the modal bandwidth (EMB) as a function of thewavelength for the MMF of FIG. 6A.

FIG. 7 illustrates a cross sectional perspective view of a core andcladding according to an embodiment of the present invention.

FIG. 8 illustrates a shape of a refractive index profile of a core andcladding according to an embodiment of the present invention.

FIG. 9A illustrates an alpha-optimum distribution and an alpha-profilevalue for an MMF according to an embodiment of the present invention.

FIG. 9B illustrates the EMB as a function of the wavelength for thefiber of FIG. 9A.

FIG. 10A illustrates an alpha-optimum distribution and an alpha-profilevalue for an MMF according to an embodiment of the present invention.

FIG. 10B illustrates the EMB as a function of the wavelength for thefiber of FIG. 10A.

FIG. 11 illustrates a flow chart representative of a method according toan embodiment of the present invention.

FIG. 12 illustrates α_(opt) values for three exemplary dopantconcentrations.

FIG. 13 illustrates an α_(opt) profile for a fiber according to anembodiment of the present invention.

FIG. 14 illustrates maximum relative group delays for the fiber of FIG.13.

FIGS. 15-17 illustrate DMD plots for the fiber of FIG. 13.

FIG. 18 illustrates an EMB summary for the fiber of FIG. 13.

FIG. 19 illustrates an α_(opt) profile for a fiber according to anotherembodiment of the present invention.

FIG. 20 illustrates maximum relative group delays for the fiber of FIG.19.

FIGS. 21-23 illustrate DMD plots for the fiber of FIG. 19.

FIG. 24 illustrates an EMB summary for the fiber of FIG. 19.

FIG. 25 illustrates a flow chart representative of a method according toanother embodiment of the present invention.

FIG. 26 illustrates a dopant concentration profile for a fiber accordingto an embodiment of the present invention.

FIGS. 27-29 illustrate DMD plots for the fiber of FIG. 26.

FIG. 30 illustrates an EMB summary for the fiber of FIG. 26.

FIG. 31 illustrates an exemplary CWDM system according to an embodimentof the present invention.

FIG. 32 illustrates operational wavelength channels for the CWDM systemof FIG. 31.

FIG. 33 illustrates attenuation for the CWDM system of FIG. 31.

FIG. 34 illustrates chromatic dispersion for the CWDM system of FIG. 31.

DETAILED DESCRIPTION

A cross-sectional view of an exemplary multimode optical fiber (MMF) inaccordance with the present invention is shown in FIG. 7. This fiberincludes a core region having a center and a radius a, and a claddingregion surrounding the core. Both the core and the cladding arecomprised of optically conductive materials such that the refractiveindex at the center of the core (n₁) is greater than the refractiveindex of the cladding (n₂), and the distribution of the refractiveindices throughout the optical fiber is generally referred to as thefiber's refractive index profile.

In an embodiment, the MMF of the present invention includes a dispersionparameter profile having a concave or a convex shape withminimum/maximum value at or near to the wavelength which has the peakEMB or λ_(p). Such an MMF can have a refractive index profile thatincludes a generally parabolic shape as shown in FIG. 8. This refractiveindex profile can be attained by including, in the core, one or moredopants in respective concentrations, and it can be defined by equation(1) where the α-value is selected pursuant the fiber's α_(opt) profile.An α-value selected pursuant to the present invention may be referred toas α_(d) through this specification.

Instances of exemplary characteristics of an MMF provided in accordancewith some embodiments of the present invention are shown in FIGS.9A-10B. FIGS. 9A and 9B illustrate exemplary characteristics of an MMFthat uses dopants such as, for example, Boron (B) to decrease therefractive index of the core and/or cladding and Fluorine (F) todecrease the refractive index of the cladding. Certain combination ofconcentrations of these dopants in the core and cladding can produceconcave like functions for the alpha optimum profile as shown by thesolid line in FIG. 9A. By designing the fiber to have a refractive indexprofile with a power exponent of α_(d)<α_(opt), it is possible tomaintain negative relative group delays over a broad spectral regionwhile maintaining a high modal bandwidth as illustrated in FIG. 9B.

FIGS. 10A and 10B illustrate exemplary characteristics of another MMFthat is doped with, for example, phosphorous (P) to increase therefractive index of the cladding. Small amounts of phosphorous, or otherdopants, in the core in combination with dopant(s) such as fluorine inthe cladding can produce convex like functions for the alpha optimumprofile as shown in FIG. 10A. By designing the fiber to have arefractive index profile with a power exponent of α_(d)<α_(opt), it ispossible to maintain negative relative group delays in a broad spectralregion while maintaining a high modal bandwidth as illustrate in FIG.10B.

FIG. 11 illustrates a flow chart outlining the process for determiningα_(d) and developing an MMF profile according to an embodiment of thepresent invention. This embodiment can be used in a design and/ormanufacturing process for an MMF with one or more dopants, where theconcentration profile of each dopant is based on the same α_(d) value.It is to be understood that the same α_(d) value does not require thesame dopant concentration value. In step 100, the initial parameters areselected for the MMF. These parameters can include, but are not limitedto, numerical aperture, index contrast Δ, core and cladding dimensions,peak EMB, maximum coupling loss, chromatic dispersion parameters (e.g.,chromatic dispersion coefficient D, zero dispersion wavelength λ_(z)),manufacturing tolerances, and/or desired spectral windows for a minimumvalue of the effective modal bandwidth EMB₀. Once the initial parametersare provided, one or more dopants together with their respectiveconcentrations are selected in step 105. The selection in step 105 maybe based on some pre-existing criteria, such as, for example, a libraryof dopants compatible for the fabrication of SiO₂ fiber core andcladding. A very brief example of such a library is provided in TableIII. The range of combinations among these and other dopants is veryextensive, and can be computed numerically from the Sellmeiercoefficients.

TABLE III Sellmeier Sellmeier Doping element coefficients coefficientsSample & concentration a_(i) b_(i) 1 Cl (~0.06 wt %) 0.50716 0.040140.59707 0.11359 0.69879 8.81674 2 Cl (0.3 wt %) 0.88671 0.07954 0.216750.1244 0.69401 8.83315 3 F (0.9 wt %) 0.87219 0.07417 Cl (0.13 wt %)0.21238 0.1298 0.94959 10.22611 4 P (12.5 wt %) 0.51512 0.02636 Cl(~0.03 wt %) 0.62804 0.11614 1.0743 10.6931 5 B2O3 (13.3 mol %) 0.6906180.0619 0.401996 0.123662 0.898817 9.09896 6 P205 (9.1 mol %) 0.695790.061568 0.452497 0.119921 0.712513 8.656641

Alternatively, the selection in step 105 may be random. Upon theselection of the dopant(s) and respective concentration(s), an initialverification step 110 is performed where the basic characteristics suchas, but not limited to, numerical aperture, Δ, D, and λ_(z) arecomputed. The initial verification can allow for a relatively earlydetermination of whether the selected material(s) will result in an MMFthat falls within some desired guidelines. This can be especially usefulin determining whether the MMF will satisfy certain standardscharacteristics such as those defined by the OM3 and OM4 standards. Thisdetermination can be made in step 115 where if it is determined that theMMF will not satisfy some predetermined criteria, a new selection of adopant(s) and concentration(s) must be made in step 105. While thisverification and comparison process embodied in the two steps 110 and115 is performed immediately after the dopant selection step of 105,this is not a requirement. Instead it may be performed during any timefollowing step 105. However, for practical purposes, early determinationof a non-compatible selection in step 105 may provide time, computing,and/or cost savings.

If at step 115 it is determined that the selected material(s) andrespective concentration(s) are satisfactory, in step 120 the profile ofthe dispersion parameter y(λ) and the optimum α-value α_(opt)(λ) arecalculated using equations (3) and (4), and in step 125 the concavity ofthe dispersion parameter y(λ) around the peak EMB λ_(p) is evaluated.Note that the term “concavity” as used herein refers to both a concaveand a convex shape. If the profile of the dispersion parameter is notconcave or convex around the peak EMB, steps 105-125 are repeated with anew dopant(s) and/or concentration(s). If, on the other hand, theprofile of the dispersion parameter does exhibit desired concavityaround the peak EMB value, the method proceeds to step 130 where anα_(d) value is chosen based on the optimum α-value at peak EMBα_(opt)(λ_(p)) and the manufacturing tolerances. In an embodiment, α_(d)follows the following equation:α_(d)=α_(opt)(λ_(p))+b·abs(T _(α))/2  (6)where T_(α) manufacturing tolerance for the α-parameter which depends onmanufacturer (e.g., ±0.01) and parameter b is utilized to increase thebroadband windows for high EMB, relax the conditions for relativenegative mode group delay tilt, to include the small dependence of alphawith wavelength, or to adjust for the different process used by fibermanufacturers. In order to produce an MMF which exhibits the L-MMFcondition, the sign of b must be negative.

In some cases, for example multicomponent fiber, it may not be possibleto find relatively simple analytical expressions such as equations (6).In those cases, use of a full numerical model to find the optimum α_(d)value for each component may be required.

After determining the α_(d) value, the relative mode group delayst_(g)(λ) are derived in step 135 by using equation (2) and substitutingα_(d) in place of α; the differential mode delay (DMD) profiles arecomputed in step 140 from the earlier-derived mode group delayst_(g)(λ); and the effective modal bandwidth EMB(λ) is computed in step145 from the earlier computed DMD profiles. Thereafter, a finalverification of performance compliance is made in step 150 where thevalues obtained in steps 135-145 are evaluated. In one example, theevaluation in step 150 can be limited to the evaluation of the EMB(λ) toverify that it is in compliance with the minimum required value EMB₀ forthe spectral window originally defined in step 100. In other examples,the values derived in steps 135 and 140 can also be evaluated. Forinstance, the maximum values for the relative mode group delays arechecked to fall within some predetermined range group (e.g., a rangespecified by the OM3 or OM4 standard). Furthermore, the sign (e.g.,positive versus negative) of the relative mode group delay values canalso be evaluated to confirm the presence of an L-MMF condition for atleast some of the operating wavelengths. In another instance, the DMDplots can be evaluated for visual confirmation of fiber's transmissioncharacteristics (e.g., the presence of a left shift of the majority ofpeak pulse at increasing radial offsets at various wavelengths).Moreover, the plots can be used to measure the DMD value at variousoperating wavelengths which in it of itself can be a prerequisite tomeeting some preexisting standard. Note that the recitation ofverification processes is not meant to be limiting and/or exhaustive. Ifthe verification process returns a favorable result, the MMF parametersare saved in step 155 for later use such as, for example, themanufacture of the MMF. If, on the other hand, the verification step 150fails, steps 105-145 are repeated for new dopant(s) and/orconcentration(s).

As an example, the method described in FIG. 11 may be used to produce abroadband MMF that uses B₂O₃ and small amounts of GeO₂. The addition ofB₂O₃ dopant to the fiber's core has the effect of reducing therefractive index and therefore reducing the Δ, increasing phase velocityand group velocity relative to pure Si, and varying the shape of thedispersion parameter y(λ) and α_(opt).

In order to maintain Δ≈1% at an operating wavelength of about 850 nm toreduce coupling losses when mated with legacy fibers, modeling resultsindicate that Fluorine doping in the cladding and/or combined doping ofGeO₂—B₂O₃ in the core may be desired. The effect of B₂O₃ on α_(opt) isshown in FIG. 12 where the wavelength-dependent α_(opt) profiles aremodeled for three dopant concentrations. The (a) α_(opt) profile isbased on a concentration of 13.3 mol % of B₂O₃; the (b) α_(opt) profileis based on a concentration of 4.1 mol % of GeO₂ and 7.7 mol % of B₂O₃;and the (c) α_(opt) profile is based on a concentration of 0.1 mol % ofGeO₂ and 5.5 mol % of B₂O₃.

To produce a broadband MMF with high modal bandwidth and negative groupdelays the required concentration of dopants should be preciselycontrolled. This may allow the negative group delay condition to bemaintained for at least 200 nm for EMB>4.7 GHz·km, and over 300 nm forOM3 fibers.

In an embodiment, the fibers that satisfy the requirements for high EMBand negative group delays can have a core with GeO₂ dopant concentrationbetween 3 to 6 mol % and B₂O₃ dopant concentration between 4 and 9 mol%. For such fiber the cladding includes a less than 4 wt % dopantconcentration of B₂O₃ and/or F. For example of the α_(opt) value of anMMF co-doped with 4.1 mol % Ge and 7.7 mol % B₂O₃ in the core, and 3 wt% F in the cladding is shown in FIG. 13 as the parabolically shapedsolid line. The ideal designed alpha (α_(d)) for the profile shape is2.1147 and is equivalent to the α value at the vertex of the parabolicplot. For this example, it is assumed that tolerances of ±0.005 in theα_(d) value (with respect to the ideal α_(d) value) are permissible inorder to remain within the desired EMB limits.

Given the potential α_(d) values shown in FIG. 13, it is possible toderive the maximum values for the relative mode group delays usingequation (2). These results are provided in FIG. 14 where the maximumrelative group delays are plotted as a function of wavelength for thethree separate target α_(d) values (α_(d)=2.1197 for triangle markers;α_(d)=2.1147 for dot markers; and α_(d)=2.1097 for square markers). Thedotted horizontal lines represent the range limits of maximum delays forEMB>4.7 GHz·km. Based on these results it is possible to tell that allthree instances remain within the maximum delay limits over a relativelybroad range of wavelengths. Furthermore, it is possible to tell that forMMFs having α_(d)=2.1147 or 2.1097, the maximum relative mode groupdelays within the region of interest have a negative value. Thisprovides an indication of an L-MMF condition occurring throughout therange of interest for the respective fibers. On the other hand, for anMMF having α_(d)=2.1197, at least some maximum relative group delayswill have a positive value. While this may not be desirable in somecases, in other cases the positive values may form a part of an overallanalysis of the performance resulting from a fiber with a certain α_(d)value. In other words the existence of positive α_(d) values does notnecessarily take the resulting fiber or the process by which that fiberwas made outside the scope of the present invention. This, as furtherdescribed later in the specification, is because at higher wavelengths,MCDC may not be of such high concern. As such, a fiber which meets theL-MMF condition over only a part of its operational wavelength windowmay still be desirable. The results provided in FIG. 14 highlight thepotential need for selecting an appropriate α_(d) value so as to remainwithin appropriate operational limits considering potentialmanufacturing tolerances.

Given the maximum relative group delays, it is then possible todetermine a series of DMD plots for a respective fiber. FIGS. 15-17 showthe DMD plots computed for the maximum relative group delays of thefiber with α_(d)=2.1147. The DMD pulses in these plots were computedusing TIA's procedure described in the FOTP-220 standard, which isincorporated herein by reference in its entirety. These plots simulatethe measured DMD pulses at each wavelength as indicated at the top ofeach figure. Having a DMD plot for a given wavelength, it is thenpossible to compute the EMB for that respective wavelength. For theexamples of FIGS. 15-17 the respective EMB values are provided at thetop of each DMD plot, and a summary of the EMB values as a function ofwavelength is provided in FIG. 18.

As another example, the method described in FIG. 11 may also be used toproduce a broadband MMF that uses P₂O₅ as the core dopant and F as thecladding dopant. The addition of P₂O₅ dopant to the fiber's core has theeffect of increasing the refractive index and therefore increasing theΔ, i.e., the difference in core-cladding refractive index, reducingphase velocity and group velocity relative to pure Si, and varying theshape of the dispersion parameter y(λ) and α_(opt). In order to maintainΔ≈1% at an operating wavelength of about 850 nm to reduce couplinglosses when mated with legacy fibers, modeling results indicate thatFluorine doping in the cladding and/or combined doping of GeO₂—P₂O₅ inthe core may be preferred. This may allow the negative group delaycondition to be maintained for at least 200 nm for EMB>4.7 GHz·km, andover 300 nm for OM3 fibers.

In an embodiment, the fibers that satisfy the requirements for high EMBand negative group delays can have a core with P₂O₅ dopant concentrationbetween 6 to 10 mol %. FIG. 19 illustrates an α_(opt) profile for afiber having a 9.1 mol % concentration of P₂O₅ and 90.9 mol %concentration of SiO₂. Based on this profile, an α_(d) is selected to be2.01205 (illustrated in FIG. 19 via a dashed line). The selected α_(d)provides a basis for deriving the maximum values for the relative modegroup delays using equation (2). The maximum relative group delays as afunction of wavelength for the target α_(d) are shown in FIG. 20, withthe horizontal dotted lines representing represent the range limits ofmaximum delays for EMB>4.7 GHz·km.

From the derived group delays, it is then possible to determine a seriesof DMD plots for a respective fiber. FIGS. 21-23 show the DMD plotscomputed for the maximum relative group delays shown in FIG. 20. The DMDpulses in these plots were computed using TIA's procedure described inthe FOTP-220 standard. These plots simulate the measured DMD pulses ateach wavelength as indicated at the top of each figure. Having a DMDplot for a given wavelength, it is then possible to compute the EMB forthat respective wavelength. For the examples of FIGS. 21-23 therespective EMB values are provided at the top of each DMD plot, and asummary of the EMB values as a function of wavelength is provided inFIG. 24.

Another method for designing an MMF according to an embodiment of thepresent invention is outlined in the flow chart of FIG. 25. Thisembodiment can be especially applicable in design and/or manufacturingprocesses of MMFs with two or more dopants where the α-value of at leastone dopant concentration profile is different from the α-value of atleast one other dopant concentration profile. An exemplaryrepresentation of a fiber having dopant concentration profiles differingwith respect to their power exponent α is illustrated in FIG. 26.However, this method can still be used to design fibers using only asingle primary dopant also.

In step 200, the initial parameters are selected for the MMF. Theseparameters can include, but are not limited to, numerical aperture,index contrast Δ, core and cladding dimensions, peak EMB, maximumcoupling loss, chromatic dispersion parameters (e.g., chromaticdispersion coefficient D, zero dispersion wavelength λ_(z)),manufacturing tolerances, and/or desired spectral windows for a minimumvalue of the effective modal bandwidth EMB₀. Once the initial parametersare provided, the dopants together with respective concentrations areselected in step 205. The selection in step 205 may be based on somepre-existing criteria, such as, for example, a library of dopantscompatible for the fabrication of SiO₂ fiber core and cladding.Alternatively, the selection in step 205 may be random.

Upon the selection of the dopants and respective concentrations, aninitial verification step 210 is performed where the basiccharacteristics such as, but not limited to, numerical aperture and Δare computed for the selected materials and concentrations. The initialverification can allow for a relatively early determination of whetherthe selected material will result in an MMF that falls within somedesired guidelines. This can be especially useful in determining whetherthe MMF will satisfy certain standards characteristics such as thosedefined by the OM3 and OM4 standards. This determination can be made instep 215 where if it is determined that the MMF will not satisfy somepredetermined criteria, a new selection of a dopants and concentrationprofiles must be made in step 205. While this verification andcomparison process embodied by the two steps 210 and 215 is performedimmediately after the dopants selection step of 205, this is not arequirement. Instead it may be performed during any time following step205. However, for practical purposes, early determination of anon-compatible selection in step 205 may provide time, computing, and/orcost savings.

If at step 215 it is determined that the selected materials andconcentrations are satisfactory, in step 220 the spectralcharacteristics of the fiber with the selected materials are modeledusing the Sellmeier coefficients given by:

$\begin{matrix}{{n^{2}(\lambda)} = {1 + {\sum\limits_{i = 1}^{3}\;\frac{a_{i}\lambda^{2}}{\lambda^{2} - b_{i}^{2}}}}} & (7)\end{matrix}$Because the concentrations of the dopants vary along the radial positionof the fiber's core, modeling of the spectral characteristics isachieved by taking this radial variance into consideration.Consequently, equation (7) becomes a function of λ and r, and also takesinto consideration that more than one dopant may be used.

After determining the spectral characteristics for the MMF, the relativemode group delays t_(g)(λ) are derived in step 225 by using numericalmodels, such as for example Wentzel—Kramer-Brillouin or Finite TimeDomain Difference; the differential mode delay (DMD) profiles arecomputed in step 230 from the earlier-derived mode group delayst_(g)(λ); and the effective modal bandwidth EMB(λ) is computed in step235 from the earlier computed DMD profiles.

Thereafter, a final verification of performance compliance is made instep 240 where the values obtained in steps 225, 230 and/or 235 areevaluated. In one example, the evaluation in step 240 can be limited tothe evaluation of the EMB(λ) to verify that it is in compliance with theminimum required value EMB₀ for the spectral window originally definedin step 200. In other examples, the values derived in steps 230 can alsobe evaluated. For instance, the DMD plots can be evaluated for visualconfirmation of fiber's transmission characteristics (e.g., the presenceof a left shift of the majority of peak pulse at increasing radialoffsets at various wavelengths). Moreover, the plots can be used tomeasure the DMD value at various operating wavelengths which in it ofitself can be a prerequisite to meeting some preexisting standard. Notethat the recitation of verification processes is not meant to belimiting and/or exhaustive. If the verification process returns afavorable result, the MMF parameters are saved in step 245 for later usesuch as, for example, the manufacture of the MMF. If, on the other hand,the verification step 240 fails, steps 205-240 are repeated for a newdopant and/or concentration.

As an example, the method described in FIG. 25 may be used to produce abroadband MMF that uses Ge and F as its dopants. FIG. 26 illustratesexemplary concentration profiles for the Ge and F dopants, with Ge mol %concentration being represented via the solid line and F mol %concentration being represented via the dotted line. Both of theseconcentrations can be represented with the following equations as afunction of radial offset r from the center of the core:

$\begin{matrix}{{{For}\mspace{14mu}{Ge}\text{:}\mspace{14mu}{X_{Ge}(r)}} = {X_{Ge}^{Max}( {1 - ( \frac{r}{a} )^{\alpha_{d}^{Ge}}} )}} & (8) \\{{{For}\mspace{14mu} F\text{:}\mspace{14mu}{X_{F}(r)}} = {X_{F}^{Max}( ( \frac{r}{a} )^{\alpha_{d}^{F}} )}} & (9)\end{matrix}$where α_(d) ^(Ge) and α_(d) ^(F) are parameters which determine theshape of the respective dopant concentration profile and X_(Ge) ^(Max)and X_(F) ^(Max) are parameters that define the maximum concentrationsof respective dopants at some radial offset position. The values forthese parameters can be selected based on some pre-existing criteria,such as, for example, generally known dopant concentrations andconcentration profile shapes, or at random. In the example of FIG. 26,the α_(d) values are selected to be α_(d) ^(Ge)=1.9963 and α_(d)^(F)=2.0093.

Taking equations (8) and (9) into consideration it is then possible togenerate the spectral characteristics of the fiber as a function ofradial offset r and wavelength λ. Expanding on equation (7), theresultant refractive index profile is computed using:

$\begin{matrix}{{n^{2}( {r,\lambda} )} = {1 + {\sum\limits_{i = 1}^{3}\;\frac{( {a_{i} + {{X_{Ge}(r)}{da}_{i}^{Ge}} + {{X_{F}(r)}{da}_{i}^{F}}} )\lambda^{2}}{\lambda^{2} - ( {b_{i} + {{X_{Ge}(r)}{db}_{i}^{Ge}} + {{X_{F}(r)}{db}_{i}^{F}}} )}}}} & (10)\end{matrix}$where X_(Ge) and X_(F) are the mole fractions, and da_(i) the db_(i) thematerial specific variation terms. Given the result-set of equation(10), it is possible to derive the maximum values for the relative modegroup delays, and then using those values to determine a series of DMDplots for the respective fiber as shown in FIGS. 27-29. The DMD pulsesin these plots were computed using TIA's procedure described in theFOTP-220 standard. These plots simulate the measured DMD pulses at eachwavelength as indicated at the top of each figure (825 nm to 1175 nm).Having a DMD plot for a given wavelength, it is then possible to computethe EMB for that respective wavelength. For the examples of FIGS. 27-29the respective EMB values are provided at the top of each DMD plot, anda summary of the EMB values as a function of wavelength is provided inFIG. 30. In these figures it is observed that the negative DMD tilt(e.g., the L-MMF) and the EMB≥4.7 GHz·km conditions can be maintainedfrom 850 nm to 950 nm.

These results indicate that using the MMF of the currently describedembodiment can be especially advantageous in the shorter wavelengthsregion of about 850 nm to about 950 nm. At longer wavelengths(e.g., >975 nm) the attenuation and chromatic dispersion can besignificantly lower accounting for a least 2 dB reduction intransmission penalties compared with the penalties at 850 nm. Therefore,at those longer wavelengths MCDC may not be required. By modifying theexponents in the dopant concentration functions shown in equations (8)and (9), the peak EMB wavelength or λ_(p) can be shifted either to theleft or to the right. For example by using α_(d) ^(Ge)=1.9963 and Δ_(d)^(F)=2.0163, λ_(p) becomes ˜900 nm.

Concepts disclosed herein can be applied to designing optical fibers foruse with laser transceivers emitting multiple transverse modes (e.g.,VCSEL transceivers). This fiber can be used in channels requiring thetransmission and receiving of multiple signals over a broad range ofwavelengths.

Concepts embodied by the present invention may be applicable inunidirectional and/or bidirectional CWDM (coarse wavelength-divisionmultiplexing). It has been recognized that performance of CWDM systemsdepend not only on modal bandwidth, but also on the total bandwidthresulting from the modal and chromatic dispersion interaction.

In order to equalize the reach or performance of the transmitterwavelength in a CWDM channel as illustrated in FIG. 31, MCDC(modal-chromatic dispersion compensation) should preferably be appliedto the shorter wavelength of the utilized spectra in such a way that thepenalties due to dispersion and attenuation are balanced. For example,FIG. 32 shows the case where n=8 wavelengths separated by Δs=40 nm. Thisconfiguration may allow 100 Gbps or 128 Gbps bidirectional transmissionper fiber by multiplexing different wavelength VCSELs with serial ratesof 25 Gbps or 28 Gbps. It may also enable 200 Gbps bidirectionaltransmission per fiber using VCSEL transceivers with serial rates of 50Gbps. Transceivers operating with the first 4 shorter wavelengths (i.e.,850 nm to 970 nm) are subject of significantly more attenuation (asshown in FIG. 33) and chromatic dispersion (as shown in FIG. 34) thantransmitters operating with the longer wavelengths. Therefore, theimpact of MCDI (modal-chromatic dispersion interaction) described hereincan be more significant for the shorter wavelengths than the longerwavelengths.

Additionally, design techniques described herein may be combined withany known fiber manufacturing techniques to the extent necessary. Forexample, those of ordinary skill will be familiar with the generalconcept of manufacturing optical fibers where in a first stage a preformis produced and in a second stage a fiber is drawn from that preform.Those familiar with the relevant art will also be familiar with thetechniques used to introduce/add one or more dopants during themanufacturing stages. This step typically occurs during the preformformation stage where a controlled introduction of dopants results in apreform having some desired dopant concentration profile. In someembodiments, it is at this stage that the selected dopants can becontrolled in accordance with the design parameters of the presentinvention. Furthermore, in some embodiments, the reference to a “broadspectral region” may be understood to refer to a region that is at least50 nm, at least 100 nm, at least 150 nm, at least 200 nm, at least 250nm, and/or at least 300 nm. However, this should not be interpreted aslimiting the meaning of the term “broad spectral region,” as in someembodiments this term may also have a customary meaning as would beunderstood by those of ordinary skill in the relevant art.

Note that while this invention has been described in terms of severalembodiments, these embodiments are non-limiting (regardless of whetherthey have been labeled as exemplary or not), and there are alterations,permutations, and equivalents, which fall within the scope of thisinvention. Additionally, the described embodiments should not beinterpreted as mutually exclusive, and should instead be understood aspotentially combinable if such combinations are permissive. It shouldalso be noted that there are many alternative ways of implementing themethods and apparatuses of the present invention. For example, whileextensive references have been made to VCSEL systems throughout thespecification, the present invention may be implemented with other,non-VCSEL optical sources. It is therefore intended that claims that mayfollow be interpreted as including all such alterations, permutations,and equivalents as fall within the true spirit and scope of the presentinvention.

Furthermore, the subject matter described herein, such as for examplethe methods for designing and/or manufacturing an MMF in accordance withthe present invention, can be implemented at least partially in softwarein combination with hardware and/or firmware. For example, the subjectmatter described herein can be implemented in software executed by aprocessor. In one exemplary implementation, the subject matter describedherein can be implemented using a non-transitory computer readablemedium having stored thereon computer executable instructions that whenexecuted by the processor of a computer control the computer to performsteps of a method or process. Exemplary computer readable media suitablefor implementing the subject matter described herein includenon-transitory computer-readable media, such as disk memory devices,chip memory devices, programmable logic devices, and applicationspecific integrated circuits. In addition, a computer readable mediumthat implements the subject matter described herein may be located on asingle device or computing platform or may be distributed acrossmultiple devices or computing platforms. Devices embodying the subjectmatter described herein may be manufactured by any means, such as bysemiconductor fabrication or discreet component assembly although othertypes of manufacturer are also acceptable, and can be manufactured ofany material, e.g., CMOS.

REFERENCES

The following references are incorporated herein in their entirety:

-   Jack Jewell, “Extended Wavelength Receivers for forward    compatibility,” Presented in T11 PI6, June 2013    ftp://ftp.t10.org/t11/document. 13/13-214 v0.pdf;-   Buck, Fundaments of Optical Fibers, Willey, April 204, ISBN:    978-0-471-22191-3;-   TIA-455-220-A, “DMD Measurement of Multimode Fiber in the Time    Domain,” January 2003;-   IEC 60793-1-49, “Measurement methods and test    procedures—Differential Mode Delay”;-   Gholami A., Molin, D., Sillard, P., “Physical Modeling of 10 GbE    Optical Communication Systems,” IEEE OSA JLT, 29(1), 2011, pp.    115-123;-   J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Investigation of    the Interaction of Modal and Chromatic Dispersion in VCSEL-MMF    Channels,” IEEE OSA JLT, 30(15), pp. 2532-2541;-   R. Pimpinella, J. Castro, B/ Kose, and B. Lane, “Dispersion    Compensated Multimode Fiber,” Proceeding of the 60th IWCS 2011;-   J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Mode Partition    Noise and Modal-Chromatic Dispersion Interaction Effects on Random    Jitter,” IEEE OSA JLT, 31(15), pp. 2629-2638;-   Marcuse, Principles of Optical Fiber Measurements, Academic Press,    NY, 1981;-   Solomon Musikant, Optical Materials, CRC Press, May 22, 1985;-   H. M. Presby and l. P. Kaminow, “Binary silica optical fibers:    refractive index and profile dispersion measurements,” Applied    Optics, Vol. 15, Issue 12, pp. 3029-3036 (1976);-   C. R. Hammond, “Silica Based Binary Glass Systems: wavelength    dispersive properties and composition in optical fibers,” Optical    and Quantum Electronics, vol, 10, pp. 163-170, 1977;-   O. V. Butov, et al. “Refractive index dispersion of doped silica for    fiber optics,”, Optics Communication, vol 213, pp. 301-308, 2002.

We claim:
 1. A multimode optical fiber (MMF) for operating within aspectral window, said MMF comprising: a cladding; and a core, said corehaving a radius a and a refractive index profile, said core comprisingat least one dopant, a concentration of said at least one dopant varyingbetween a center of said core and a, wherein said spectral window isdefined by an overlapping range of wavelengths (1) at which said MMF hasan effective modal bandwidth (EMB) equal to or above a predefinedminimum with one of a peak EMB or a minimum EMB occurring at wavelengthλ_(p) which is less than a maximum wavelength of said spectral windowand (2) at which a differential mode delay (DMD) plot of said MMFexhibits a shift to the left of its higher order modes relative to itslower order modes, wherein said DMD plot is measured by launching aplurality of optical pulses into one end of said core at various radialdistances r and observing an arrival of said optical pulses at anotherend of said core at said various radial distances r to determine avelocity of any one of said plurality of optical pulses launched intosaid core at some radial distance r relative to any other of saidplurality of optical pulses launched into said core at some other radialdistance r, and wherein said shift to the left is characterized by someof said plurality of optical pulses having a faster velocity relative toat least one other optical pulse having a slower velocity, said at leastone other optical pulse having a slower velocity being launched intosaid core at a lower radial distance r than any of said some of saidplurality of optical pulses having a faster velocity wherein saidrefractive index profile is characterized by a predefined value α,wherein said core includes α_opt profile comprised of values α_opt(λ)defined by a function of wavelength λ, wherein for a given λ saidα_opt(λ) value minimizes a group delay of said MMF when said α is setequal to α_opt(λ), said α_opt profile having one of a concave shape witha maximum α_opt value or a convex shape with a minimum α_opt value, andwherein α is less than or equal to said one of said maximum α_opt valueor said minimum α_opt value.
 2. The MMF of claim 1, wherein said atleast one other optical pulse having a slower velocity is launched intosaid core at a radial distance of 5 microns.
 3. The MMF of claim 1,wherein said predefined minimum is 4700 MHz·km.
 4. The MMF of claim 1,wherein said spectral window is at least 50 nm.
 5. The MMF of claim 1,wherein said spectral window is at least 100 nm.
 6. The MMF of claim 1,wherein said spectral window is at least 200 nm.
 7. The MMF of claim 1,wherein said α_(opt) profile has one of said concave shape with saidmaximum α_(opt) value=α_(opt)(λ_(p)) or said convex shape with saidminimum α_(opt) value=α_(opt)(λ_(p)).
 8. The MMF of claim 1, whereinsaid core includes a dispersion parameter profile defined by a functionof wavelength λ, said dispersion parameter profile having one of aconcave shape with a maximum or a convex shape with a minimum.
 9. TheMMF of claim 8, wherein said dispersion parameter profile has one ofsaid concave shape with said maximum at occurring at λ_(p) or saidconvex shape with said minimum occurring at λ_(p).